If the length of a rectangle in terms of x
is 3x^2 +7x +9
, and its width is 3x +6
, what is the perimeter of this rectangle?
The formula for perimeter of a rectangle is:
P = 2(length + width)
Substituting the given expressions:
P = 2(3x^2 + 7x + 9 + 3x + 6)
Simplifying:
P = 6x^2 + 16x + 30
Therefore, the perimeter of the rectangle is 6x^2 + 16x + 30.
To find the perimeter of a rectangle, we need to add up all four sides.
Given that the length of the rectangle is 3x^2 + 7x + 9 and the width is 3x + 6, we can determine the four sides of the rectangle.
The length of the rectangle is represented by 3x^2 + 7x + 9. Since there are two equal length sides, each side length will be (3x^2 + 7x + 9) / 2.
The width of the rectangle is represented by 3x + 6. Since there are two equal width sides, each width length will be (3x + 6) / 2.
To find the perimeter, we add up all four sides:
Perimeter = 2 * (length + width)
= 2 * ((3x^2 + 7x + 9) / 2 + (3x + 6) / 2)
= 2 * ((3x^2 + 7x + 9 + 3x + 6) / 2)
= (6x^2 + 14x + 18 + 6x + 12) / 2
= (6x^2 + 20x + 30) / 2
= 3x^2 + 10x + 15
Therefore, the perimeter of the rectangle is 3x^2 + 10x + 15.